Model Atmosphere Results (Kurucz 1979, ApJS, 40, 1)

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Model Atmosphere Results(Kurucz 1979, ApJS, 40,
1)

• Kurucz ATLAS LTE codeLine BlanketingModels,
  SpectraObservational Diagnostics

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ATLAS by Robert Kurucz (SAO)

• Original paper and updated materials
  (kurucz.cfa.harvard.edu) have had huge impact on
  stellar astrophysics
• LTE code that includes important continuum
  opacity sources plus a statistical method to deal
  with cumulative effects of line opacity (line
  blanketing)
• Other codes summarized in Gray

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ATLAS Grid

• Teff 5500 to 50000 KNo cooler models since
  molecular opacities largely ignored.Models for
  Teff gt 30000 K need non-LTE treatment (also in
  supergiants)
• log g from main sequence to lower limit set by
  radiation pressure (see Fitzpatrick 1987, ApJ,
  312, 596 for extensions)
• Abundances 1, 1/10, 1/100 solar

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Line Blanketing and Opacity Distribution
Functions

• Radiative terms depend on integrals
• Rearrange opacity over intervalDF fraction of
  interval with line opacity lt l?
• Same form even with many lines in the interval

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ODF Assumptions

• Line absorption coefficient has same shape with
  depth (probably OK)
• Lines of different strength uniform over interval
  with near constant continuum opacity (select
  freq. regions carefully)

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ODF Representation

• DF as step functions
• Pre-computed for grid over range in
  temperatureelectron densityabundancemicroturbul
  ent velocity(range in line opacity)

T 9120 K
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Line Opacity in Radiation Moments
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Atmospheric Model Listings

• Tables of physical and radiation quantities as a
  function of depth
• All logarithms except T and 0 (c.g.s.)

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Emergent Fluxes ( Intensities)
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Temperature Relation with Line Blanketing

• With increased line opacity, emergent flux comes
  from higher in the atmosphere where gas is cooler
  in general lower I?, J?
• Radiative equilibrium lower J? ? lower T
• Result surface cooling relative to models
  without line blanketing

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Temperature Relation with Line Blanketing

• To maintain total flux need to increase T in
  optically thick part to get same as gray case
• Result backwarming

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Flux Redistribution (UV?optical)opt. F?
hotter unblanketed model
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Temperature Relation with Convection

• Convection
• Reduces T gradient in deeper layers of cool
  stars

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Geometric Depth Scale

• Physical extent large in low density cases
  (supergiants)

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Observational Parameters

• Colors Johnson UBVRI, Strömgren ubvy (Lester et
  al. 1986, ApJS, 61, 509)
• Balmer line profiles (Ha through Hd)

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Flux Distributions

• Wien peak
• Slope of Paschen continuum (3650-8205)
• Lyman jump at 912 (n1)Balmer jump at 3650
  (n2)Paschen jump at 8205 (n3)
• Strength of Balmer lines

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H 912
He I 504
He II 227
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Comparison to Vega
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IDL Quick Look

• IDLgt kurucz,teff,logg,logab,wave,flam,fcontINPUT
  
• teff effective temperature (K, grid value)
• logg log gravity (c.g.s, grid value)
• logab log abundance (0,-1,-2)OUTPUT
• wave wavelength grid (Angstroms)
• flam flux with lines (erg cm-2 s-1 Angstrom-1)
• fcont flux without lines
• IDLgt plot,wave,flam,xrange3300,8000,xstyle1

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Limb DarkeningEddington-Barbier Relationship
SB(t0)
SB(t1)
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How Deep Do We See At µ1? Answer Depends on
Opacity
T(t1)low opacity
T(t1)high opacity
T(t0)
Limb darkening depends on the contrast between
B(T(t0)) and B(T(t1))
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Limb Darkening versus Teff and ?

• Heyrovský 2007, ApJ, 656, 483, Fig.2
• u increases with lower ?, lower Teff
• Both cases have lower opacity ? see deeper,
  greater contrast between T at t0 and t1

Linear limb-darkening coefficient vs Teff for
bands B (crosses), V (circles), R (plus signs),
and I (triangles)